Boolean grammars: expressive power and parsing algorithms
Bibliographic record
Abstract
Context-free grammars are extended with Boolean operations, yielding a new language specification formalism named Boolean grammars. By virtue of having been produced out of two intuitively clear fundamental concepts, Boolean grammars retain some of their genuine clarity, at the same time allowing to express more than could be expressed using the context-free grammars. The semantics of the formalism is defined using language equations. As a by-product of this definition, the fundamentals of the theory of language equations with Boolean operations are established. Various sample grammars are given, ranging from the descriptions of the standard examples of non-context-free languages to a complete specification of the syntax of a simple imperative programming language. This shows Boolean grammars to be a sufficiently potent tool for language specification. At the same time, the major context-free parsing techniques, such as recursive descent, generalized LR and the Cocke-Kasami-Younger tabular algorithm, are demonstrated to have extensions for Boolean grammars. Several practically usable parsing algorithms for Boolean grammars are constructed and implemented in a research-oriented parser generator. It is shown that the increased expressive power of Boolean grammars does not demand sacrifices in terms of parsing complexity. It is proved that the languages generated by Boolean grammars are context-sensitive. One more class of grammars, called dual concatenation grammars, is introduced and shown to be equivalent to Boolean grammars. A subclass of Boolean grammars, the linear Boolean grammars, is shown to be computationally equivalent to trellis automata and to linear conjunctive grammars.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".